Related papers: A Las Vegas Rewriting Algorithm for the Symmetric …
If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank $>1$, other than any $^2F_4(q)$, over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism.…
We present a new algorithm for constructive recognition of the Suzuki groups in their natural representations. The algorithm runs in Las Vegas polynomial time given a discrete logarithm oracle. An implementation is available in the Magma…
In this paper, we describe a new Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The algorithm depends on a property of the group of rational points of an elliptic curve and is thus not a generic algorithm. The…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic. Experiments with an implementation in OSCAR with various…
We give a uniform construction of irreducible polynomial representations of all classical groups, including spin groups, using semistandard domino tableaux. We also give an explicit decomposition of the homogeneous coordinate ring of the…
Under the assumption of a certain conjecture, for which there exists strong experimental evidence, we produce an efficient algorithm for constructive membership testing in the Suzuki groups Sz(q), where q = 2^{2m + 1} for some m > 0, in…
Let Omega be a quasisimple classical group in its natural representation over a finite vector space V, and let Delta be its normaliser in the general linear group. We construct the projection from Delta to Delta/Omega and provide fast,…
Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…
We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group…
Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a $2$--complex -- the Squier complex -- whose fundamental groupoid then describes the…
The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$.…
We present practical algorithms for generating universal cycles uniformly at random. In particular, we consider universal cycles for shorthand permutations, subsets and multiset permutations, weak orders, and orientable sequences.…
Given graphs as input, Graph Neural Networks (GNNs) support the inference of nodes, edges, attributes, or graph properties. Graph Rewriting investigates the rule-based manipulation of graphs to model complex graph transformations. We…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
Quantum lambda calculus has been studied mainly as an idealized programming language -- the evaluation essentially corresponds to a deterministic abstract machine. Very little work has been done to develop a rewriting theory for quantum…
We introduce a method to enforce some symmetries starting from a trial wave-function prepared on quantum computers that might not respect these symmetries. The technique eliminates the necessity for performing the projection on the quantum…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…